Calculating Solubility

Frequently we find that the experimentally determined solubility of an ionic solid is larger than that predicted from /Qp. Consider, for example, PbCl2, where the solubility calculated from the relation... 

Fig. 10. The mole fraction of carbon dioxide in saturated solutions in air at — 110°C (above the lower critical end point). The full line is the experimental curve of Webster and the dashed curves are 1, an ideal gas mixture 2, an ideal gas mixture with Poynting s correction and 3, the solubility calculated from Eq. 8 and the principle of corresponding states.

A classic pharmaceutical science textbook might have defined poor solubility as anything below a solubility of 1 g mL-1 (2 mol L-1 solution for a molecular weight of 500 Da) at pH 6.5 (or pH 7). This classic view is reflected in the Chemical Abstracts SciFinder 2001 solubility range definitions for solubility calculated using Advanced Chemistry Development (ACD) Software Solaris V4.67. These semi-quantitative ranges for molar solubility are very soluble, 1 mol L 1 < solubility soluble, 0.1 mol L 1 < solubility < 1 mol L 1 slightly soluble, 0.01 mol L 1 <... 

KowWin aqueous solubility calculator is available at http //www.epa.gov/ oppt/exposure/docs/episuitedl.htm. 

Pure fullerenes are insoluble in aqueous environments and only sparingly soluble in many organic solvents. The greatest solubility is found in 1,2,4-trichlorobenzene (20 mg/ml), carbon disulfide (12 mg/ml), toluene (3.2 mg/ml), and benzene (1.8 mg/ml) (Wikipedia.org). Solubility calculations have been performed on (T, in 75 different organic solvents (Sivaraman et al., 2001). 

Wolery, T. J., 1983, Eq3nr, a computer program for geochemical aqueous speciat-ion-solubility calculations user s guide and documentation. Lawrence Livermore National Laboratory Report UCRL-53414. 

FIGURE 6.33 Impurities may be taken into consideration when evaluating solubility with a /iPLC system. For solubility calculations, only the peak area of the analyte of interest is used for interpolation within the corresponding external standard calibration curve. 

Sol id Sol utions. The aqueous concentrations of trace elements in natural waters are frequently much lower than would be expected on the basis of equilibrium solubility calculations or of supply to the water from various sources. It is often assumed that adsorption of the element on mineral surfaces is the cause for the depleted aqueous concentration of the trace element (97). However, Sposito (Chapter 11) shows that the methods commonly used to distinguish between solubility or adsorption controls are conceptually flawed. One of the important problems illustrated in Chapter 11 is the evaluation of the state of saturation of natural waters with respect to solid phases. Generally, the conclusion that a trace element is undersaturated is based on a comparison of ion activity products with known pure solid phases that contain the trace element. If a solid phase is pure, then its activity is equal to one by thermodynamic convention. However, when a trace cation is coprecipitated with another cation, the activity of the solid phase end member containing the trace cation in the coprecipitate wil 1 be less than one. If the aqueous phase is at equil ibrium with the coprecipitate, then the ion activity product wi 1 1 be 1 ess than the sol ubi 1 ity constant of the pure sol id phase containing the trace element. This condition could then lead to the conclusion that a natural water was undersaturated with respect to the pure solid phase and that the aqueous concentration of the trace cation was controlled by adsorption on mineral surfaces. While this might be true, Sposito points out that the ion activity product comparison with the solubility product does not provide any conclusive evidence as to whether an adsorption or coprecipitation process controls the aqueous concentration. 

The system can help scientists reliably determine what type of formulation to make. However, the only branch of the decision tree which has rules is the emulsifiable concentrates (EC) branch. The system can determine which solvents to try to make an EC. Its decision relies heavily on rules and solubility calculations. Work is just beginning on the rules to determine which emulsifiers to use. 

Since [Fe(lll)]jojaj [Fe " ], the formation of ion pairs and complexes is greatly enhancing the equilibrium solubility of ferrihydrite. This is called the salting-in effect and illustrates why mineral solubility calculations in seawater must take ion speciation into consideration. 

Solubility data for mucus are not available, but Table 7-1 indicates that the Henry s law constant for ozone in water under the conditions of the lung is 9,700. Solubility data for pure ozone and other physical properties are available from various sources. Air Quality Criteria for Photochemical Oxidants reports an ozone solubility of 0.494 ml/ 100 ml of water at 0 C for ozone at 760 mm Hg extrapolation of data from Thorp indicates 1.09 g/liter of water at 0 C and approximately 0.31 g/liter of water at 37 C for 100% ozone. The value for 37 C agrees closely with the solubility calculated from the Henry s law constant for pure ozone at 760 mm Hg. 

Ekberg, Ch. Uncertainties in Actinide Solubility Calculations Illustrated Using the Th—0H—P04 System, Diss. Chalmers tekniska hogskola, GSteborg, 1999. 

Wolery T. I (1983). EQ3NR. A Computer Program for Geochemical Aqueous Speciation-Solubility Calculations User s Guide and Documentation Lawrence Livermore Laboratory, Livermore, Cal., UCRL-53414. 

Practice a solubility calculation using silver carbonate (Ag2C03) as the solute. Dissocation of the salt yields 3 aqueous ions ... 

Fig. 9. Experimental solubilities as total uranium concentration in solution for experiments on dissolution of uraninite samples from Oklo and Cigar Lake. Solid lines correspond to the calculated solubilities. Calculations performed with PHREEQC geochemical code (Parkhust Appelo 1999) and uranium database taken from Grenthe et al. (1992) and Bruno Puigdomenech (1989).

Two different approaches have been taken by researchers to determine the secondary mineralogy of CCBs (1) direct observation, which is accomplished via analysis of weathered ash materials, and (2) prediction, based on chemical equilibrium solubility calculations for ash pore-waters and/or experimental ash leachate or extractant solutions. Because the secondary phases are typically present in very low abundance, their characterization by direct analysis is difficult. On the other hand, predictions based on chemical equilibrium modelling or laboratory leaching experiments may not be reliable indicators of element leachability or accurately indicate the secondary phases that will form under field conditions (Eighmy et al. 1994 Janssen-Jurkovicova et al. 1994). 

The so-called subcooled liquid approach was also suggested in the literature in order to overcome the difficulties connected with the pure component properties of the solid compound. This approach is commonly used for the calculation of the liquid-solid equilibria, and for solubility calculation of solids in supercritical fluids was already suggested [2] and subsequently extensively applied to different supercritical fluid processes [63]. The solubility y>2 is then expressed as ... 

From Chapters 4, 5 and 6 thermodynamic data and predictions, the maximum methane concentration (solubility) occurs in the aqueous liquid at equilibrium with hydrates. In order for methane to exsolve the liquid, the solubility must change rapidly as the water rises with corresponding decreases in pressure and temperature. Solubility calculations (Handa, 1990) indicate a change in methane concentration too gradual to account for a significant hydrate amount. Solubility data are needed at conditions of hydrate formation, in order to confirm this model. Preliminary solubility data are available from Besnard et al. (1997). 

Figure 2.27 Solubilities as a function of critical temperature (Tc) for a typical glassy polymer (polysulfone) and a typical rubbery polymer (silicone rubber) compared with values for the ideal solubility calculated from Equation (2.97)[43]...

Enhancement factors are given In Table 2. Solid densities and sublimation pressures used In the solubility calculations (Eq. 2) are given In Table 3. The densities were supplied by the manufacturers whereas the sublimation pressures were extrapolated... 

It should be noted that either the insertion or annihilation of the particle can be used to calculate the Gibbs energy of solvation, and both are related by a change of sign. With an appropriate method for solving the solubility calculations in aqueous solution, such as the one presented here, one can parameterize a model of C02 for a particular water model to reproduce these values over an extended thermodynamic window, such as over a desired temperature range that would encompass any type of brine aquifer. 

To finalize the development of the aqueous CO2 force field parameters, the C02 model was used in free energy perturbation Monte Carlo (FEP/MC) simulations to determine the solubility of C02 in water. The solubility of C02 in water is calculated as a function of temperature in the development process to maintain transferability of the C02 model to different simulation techniques and to quantify the robustness of the technique used in the solubility calculations. It is also noted that the calculated solubility is based upon the change in the Gibbs energy of the system and that parameter development must account for the entropy/enthalpy balance that contributes to the overall structure of the solute and solvent over the temperature range being modeled [17]. 

Accurate self-consistent thermochemical data for the copper chlorides up to 200°C are required, in order to improve solubility calculations and electrochemical modelling capabilities for Aspen Plus and OLI software. Experimental work has been initiated at the University of Guelph, Canada and UOIT to determine a comprehensive thermochemical database, for solubility limits of OMIT, and aqueous cupric chloride versus chloride concentration and temperature using UV-VIS spectroscopy (Suppiah, 2008). The chloride ion is obtained by adding LiCl OMIT. The conditions of tests are primarily 25-200°C, up to 20 bars. Specialised equipment for this task is needed to reach elevated temperatures and pressures, because cupric chloride is chemically aggressive, and because changes in the solution concentrations must be made precisely. A titanium test cell has been custom made, including a UV-VIS spectrometer with sapphire windows, HPLC pumps and an automated injection system. The data acquired will be combined with past literature data for the cuprous chloride system to develop a self-consistent database for the copper (I) and copper (II) chloride-water systems. 

Equation (4.4) shows that the melting point is an important determinant in solubility calculations, the lower the melting point, the lower the inter-molecular forces, and therefore the easier it is for the drug to dissolve in the intercellular lipids of the skin. It is interesting to note that two of the successful transdermally delivered drugs, nitroglycerin and nicotine, are low melting point materials. 

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